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Thanks to the theory of determinants over an Ore domain, also calledAdjamagbo determinant by the Russian school of non commutative algebra, weextend to any Weyl algebra over a field of characteristic zero Suslin theoremsolving what Suslin himself called the $K_1$-analogue of the well-known SerreConjecture and asserting that for any integer $n$ greater than 2, any $n$ by$n$ matrix with coefficients in any algebra of polynomials over a field andwith determinant one is the product of elementary matrices with coefficients inthis algebra

Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras